Last Updated 14 Apr 2020

Explanation of Modern Physics

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Explanation of Modern Physics While the term “modern physics” often suggests that all that came before it was incorrect, 20th and 21st century additions to physics simply modified and expanded the phenomena which Newton and his fellow scientists had already contrived. From the mid-1800’s onward, new advances were made in the way of physics, specifically the revolutions of Einstein’s relativity, removing mankind further from the absolute, and quantum mechanics, which replaced certainty with probability. All of this led to an advance in nuclear weaponry, the advancement of laser technology, and the information age of computers.

Although it directly contradicted the classical equipartition theorem of energy, black body radiation was one of the first discoveries in modern quantum mechanics. This theorem states that within thermal equilibrium, where each part of the system is the same temperature, each degree of freedom has 12kBT, kB representing the Boltzmann constant, of thermal energy associated with it, meaning that the average kinetic energy in the translational movement of an object should be equal to the kinetic energy of its rotational motion.

By this point, it was known how heat caused the atoms in solids to vibrate and that atoms were patterns of electrical charges, but it was unknown how these solids radiated the energy that they in turn created. Hertz and other scientists experimented with electromagnetic waves, and found that Maxwell’s previous conjectures that electromagnetic disturbances should propagate through space at the speed of light had been correct. This led to the explanation of light itself as an electromagnetic wave.

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From this observation, it was assumed that as a body was heated, the atoms would vibrate and create charge oscillations, which would then radiate the light and the additional heat that could be observed. From this, the idea of a “black body” formed, an object that would absorb all radiation that came in contact with it, but which also was the perfect emitter. The ideal black body was a heated oven with a small hole, which would release the radiation from inside.

Based on the equipartition theorem, such an oven at thermal equilibrium would have an infinite amount of energy, and the radiation through the hole would show that of all frequencies at once. However, when the experiment was actually performed, this is not the result that occurred. As the oven heated, different frequencies of radiation were detected from the hole, one at a time, starting with infrared radiation, followed by red, then yellow light, and so on.

This proved that high oscillators are not excited at low temperatures, and that equipartition was not accurate. This discovery led to Stefan’s Law, which said that the total energy per square unit of black body per unit time, the power, is proportional to the absolute temperature to the fourth power. It also led to Wien’s Displacement Law, stating that the wavelength distributions of thermal radiation of a black body at all temperatures have essentially the same shape, except that the graphs are displaced from each other.

Later on, Planck characterized the light coming from a black body and derived an equation to predict the radiation at certain temperatures, as shown by the diagram below. For each given temperature, the peaks changed position, solidifying the idea that different temperatures excite different levels of the light spectrum. This was all under the assumption that radiation was released in quanta, now known as photons. All of these laws help modern physicists interpret radiation and make accurate estimations at the temperature of planets based on the radiation that comes from them.

Einstein used the same quantization of electromagnetic radiation to show the photoelectric effect, which disproved the idea that more intense light would increase the kinetic energy of the electrons radiated from an object. Photoelectric effect was originally the work of Heinrich Hertz, but was later taken on by Albert Einstein. Einstein determined that light was made up of packets of energy known as photons, which have no mass, but have momentum and energy given by the equation E=hf, h representing Planck’s constant and f representing the frequency of the light used.

Photoelectric effect explains that if light is shone on a metal with high enough energy, electrons will be released from the metal. Due to the energy equation, light of certain low frequencies will not cause the emission of electrons, not matter how intense, while light of certain high frequencies will always emit electrons, even at a very low intensity. The amount of energy needed to release electrons from a metal plate is dependent upon the type of metal it is, and changes from case to case, as every type of metal has a certain work function, or an amount of energy needed to remove an electron from its surface.

If the photons that hit the metal plate have enough energy as the work function of the metal, the energy from the photon can transfer to an electron, which allows it to escape from the surface of the metal. Of course, the energy of the photon is dependent upon the frequency of the light. Einstein postulated that the kinetic energy of the electron once it has been freed from the surface can be written as E=hf-W, W being the work function of the material. Prior to Einstein’s work in photoelectric effect, Hertz discovered, mostly by accident, that ultraviolet light would knock electrons off of metal surfaces.

However, according to the classical wave theory of light, intensity of light changed the amplitude, thus more intense light would make the kinetic energy of the electrons higher as they were emitted from the surface. His experiment showed that this was not the case, and that frequency affected the kinetic energy, while intensity determined the number of electrons that were released. By explaining the photoelectric effect, scientists find that light is a particle, but it also acts as a wave. This help support particle-wave duality.

In order to explain the behavior of light, you must consider its particle like qualities as well as its wave like qualities. This means that light exhibits particle-wave duality, as it can act as a wave and a particle. In fact, everything exhibits this kind of behavior, but it is most prominent in very small objects, such as electrons. Particle-wave duality is attributed to Louis de Broglie in about 1923. He argued that since light could display wave and particle like properties, matter could as well.

After centuries of thinking that electrons were solid things with definite positions, de Broglie proved that they had wave like properties by running experiments much like Young’s double slit experiments, and showing the interference patterns that arose. This idea helped scientists realize that the wavelength of an object diminishes proportionally to the momentum of the object. Around the same time that de Broglie was explaining particle-wave duality, Arthur Compton described the Compton effect, or Compton scattering.

This was another discovery which showed how light could not solely be looked at as a wave, further supporting de Broglie’s particle-wave duality. Compton scattering is a phenomenon that takes place when a high-energy photon collides with an electron, causing a reduced frequency in the photon, leading to a reduced energy. Compton derived the formula to describe this occurrence to be ? '-? =hCme1-cos? = ? c(1-cos? ), where ? ' is the resulting wavelength of the photon, ? is the initial wavelength of the photon, ? is the scattering angle between the photon and the electron, and ? c is the wavelength of a resting electron, which is 2. 26 ? 10-12 meters. Compton came about this by considering the conservation of momentum and energy. Although they have no mass, photons have momentum, which is defined by ? =Ec=hfc=h?. In order to conserve momentum, or to collide at all, light must be thought of as a particle in this case, instead of a wave. Quantum mechanics is not the only facet of modern physics, and it shares equal importance with relativity. Relativity is defined as the dependence of various physical phenomena on relative motion of the observer and the observed objects, especially in relation to light, space, time, and gravity.

Relativity in modern physics is hugely attributed to the work of Albert Einstein, while classical relativity can be mainly attributed to Galileo Galilei. The quintessential example of Galilean relativity is that of the person on a ship. Once the ship has reached a constant velocity, and continues in a constant direction, if the person is in the hull of the ship and is not looking outside to see any motion, the person cannot feel the ship moving. Galileo’s relativity hypothesis states that any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments.

This idea led to the realization that velocity does not exist without a reference point. This idea of a frame of reference became very important to Einstein’s own theories of relativity. Einstein had two theories of relativity, special and general. He published special relativity in 1905, and general relativity in 1916. His Theory of Special Relativity was deceptively simple, as it mostly took Galilean relativity and reapplied it to include Maxwell’s magnetic and electric fields. Special relativity states that the Laws of Physics are the same in all inertial frames.

An inertial frame is a frame in which Newton’s law of inertia applies and holds true, so that objects at rest stay at rest unless an outside force is applied, and that objects in motion stay in motion unless acted upon by an outside force. The theory of relativity deals with objects that are approaching the speed of light, as it turns out that Newton’s laws begin to falter when the velocity gets too high. Special relativity only deals with the motion of objects within inertial frames, and is quite comparable to Galilean relativity, with the addition of a few new discoveries, such as magnetic and electric fields and the speed of light.

The theory of general relativity is much more difficult to understand than special relativity due to the fact that it involves objects traveling close to the speed of light within non-inertial frames, or frames that do not meet the requirements given by Newton’s law of inertia. General relativity coincides with special relativity when gravity can be neglected. This involves the curvature of space and time, and the idea that time is not the definite that we have always assumed that it was. General relativity is a theory that describes the behavior of space and time, as well as gravity.

In general relativity, space-time becomes curved at the presence of matter, which means that particles moving with not external forces acting upon them can spiral and travel in a curve, which becomes conflicting with Newton’s laws. In classical physics, gravity is described as a force, and as an apple falls from a tree, gravity attracts it to the center of the Earth. This also explains the orbit of planets. However, in general relativity, a massive object, such as the sun, curves space-time and forces planets to revolve around it in the same way a bead would spiral down a funnel.

This idea of general relativity and the curvature of space-time led scientists to realize what black holes were and how they can be possible. This also explains the bending of light around objects. Black holes have massive centers and are hugely dense. Each particle that it includes is also living in space-time however, and so the center must continue to move and become more and more dense from the motion of these particles. Black holes are so dense that they bend space-time to an enormous degree, so that there is no escapable route from them.

General relativity also explains that the universe must be either contracting or expanding. If all the stars in the universe were at rest compared to one another, gravity would begin to pull them together. General relativity would show that the space as a whole would begin to shrink and the distances between the stars would do the same. The universe could also technically be expanding, however it could never be static. In 1929, Hubble discovered that all of the distant galaxies seemed to be moving away from us, which would support the explanation that our galaxy is expanding.

The basis of general relativity is the dynamic movement of space and time, and the fact that these are not static measurements that they have always been assumed to be. However, a key issue is that there has been little success in combining quantum mechanics and Einsteinian relativity, other than in quantum electrodynamics. Quantum electrodynamics, QED, is a quantum theory that involves the interaction of charged particles and the electromagnetic field. The scientific community hugely agrees upon QED, and it successfully unites quantum mechanics with relativity.

QED mathematically explains the relationships between light and matter, as well as charged particles with one another. In the 1920’s, Paul Dirac laid the foundations of QED by discovering the equation for the spin of electrons, incorporating both quantum mechanics and the theory of special relativity. QED was further developed into the state that it is today in the 1940’s by Richard Feynman. QED rests on the assumption that charged particles interact by absorbing and emitting photons, which transmit electromagnetic forces. Photons cannot be seen or detected in anyway because their existence violates the conservation of energy and momentum.

QED relies heavily on the Hamiltonian vector field and the use of differential equations and matrices. Feynman created the Feynman diagram used to depict QED, using a wavy line for photons, a straight line for the electron, and a junction of two straight lines and one wavy line to represent the absorption or emission of a photon, show below. QED helps define the probability of finding an electron at a certain position at a certain time, given its whereabouts at other positions and times. Since the possibilities of where and when the electron can emit or absorb a photon are infinite, this makes this a very difficult procedure.

Compton scattering is very prevalent to QED due to its involvement in the scattering of electrons. Modern physics is a simple term used to cover a huge array of different discoveries made over the past two hundred years. While the two main facets of modern physics are quantum mechanics and relativity, there are an amazing number of subtopics and experiments that have brought about rapid change, giving the world new technologies and new capabilities. Thanks to scientists like Einstein, Hawking, Feynman, and many others, we have found, and will continue to find, amazing discoveries about our universe.

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